Practice Set - Week 2

Author

SOPHAS

Published

24-Apr-2025

Q1. The pass result of 50 students who took a class test is given below:

Marks	No of students
40	8
50	10
60	9
70	6
80	4
90	3

If the mean marks for all the students were 51.6, find out the mean marks of the students who failed.

# Answer

Q2. The average dividend declared by a group of 10 pharma companies was 18 per cent. Later on, it was discovered that one correct figure, 12, was misread as 22. Find the correct average dividend.

# Answer

Q5. Average marks section A of class 9 is 70 and average marks of section B of class 9 is 80. Find the average marks of class 9, assuming:

Both sections have equal students
There are 55 students in section A and there 45 students in section B

# Answer

Q6. $x_1$, $x_2$, $…$, $x_n$ are $n$ values. We are to calculate sum of squared deviation around a number $a$ as follows:

\[ SSD = (x_1 - a)^2 + (x_2 - a)^2 + … + (x_n - a)^2 \]

Show that $SSD$ is minimum when a is the mean of the given values.

# Answer

Q7. Median is not affective by extreme values. Give examples in support of your answer.

# Answer

Q8. Somnath does data analysis for a company. The data on tea consumption (in grams) for the company are as follows:

14.77 16.11 16.11 15.05 15.99 14.91 15.27 16.01 15.75 14.89 16.05 15.22 16.02 15.24 16.11 15.02

Calculate the mean and median tea consumption.
Which of the mean and median measures is best to use? Explain

# Answer

Q9. Following are the responses from 55 employees to the question about how much time they travel to reach the office (in mins).

055 060 080 080 080 085 085 085 090 090 090

090 092 094 095 095 095 095 100 100 100 100

100 100 105 105 105 105 109 110 110 110 110

112 115 115 115 115 115 120 120 120 120 120

124 125 125 125 130 130 140 140 140 145 150

Calculate the range and interquartile range and interpret your result.

# Answer

Q10. An agriculture farm sells grab bags of flower bulbs. The bags are sold by weight; thus the number of bulbs in each bag can vary depending on the varieties included.

Below are the number of bulbs in each of the 20 bags sampled:

21 33 37 56 47 25 33 32 47 34

36 23 26 33 37 26 37 37 43 45

What are the mean and median number of bulbs per bag?
Based on your answer, what can you conclude about the shape of the distribution of number of bulbs per bag?

# Answer

Q11. The wholesale prices of a commodity for a week are as follows:

Days: 1 2 3 4 5 6 7

Commodity price/kg: 240 260 270 245 255 286 264

Calculate the variance and standard deviation.

# Answer

Q12. (Continue from Q11) Suppose for next week, price/kg is just 10 more than previous week.

Calculate the variance and standard deviation. What is your conclusion?

# Answer

--- title: "Practice Set - Week 2" execute: error: false echo: true engine: julia date: today date-format: "DD-MMM-YYYY" author: - SOPHAS code-annotations: hover format: html: include-in-header: text: | <style> .header-container { width: 100%; } .logo { display: block; width: 150px; margin-left: -2.5%; } </style> <link rel = "icon" href="../logo/html-logo.jpg" sizes="32x32" /> include-before-body: text: | <div class="header-container"> <img src= "../logo/sophas-logo.png" width="240" height="90"> </div> self-contained-math: true anchor-sections: true toc: true toc-depth: 4 toc-expand: 2 toc-title: Contents number-sections: true code-summary: Show/Hide Code code-overflow: wrap code-tools: caption: Download tutorial source: true fig-format: svg fig-width: 8 fig-height: 6 self-contained: true --- Q1. The pass result of 50 students who took a class test is given below: | Marks | No of students| |-------|---------------| | 40 | 8 | | 50 | 10 | | 60 | 9 | | 70 | 6 | | 80 | 4 | | 90 | 3 | If the mean marks for all the students were 51.6, find out the mean marks of the students who failed. ```{julia} # Answer ``` ------------------------------------------------------------------------------------------- Q2. The average dividend declared by a group of 10 pharma companies was 18 per cent. Later on, it was discovered that one correct figure, 12, was misread as 22. Find the correct average dividend. ```{julia} # Answer ``` --------------------------------------------------------------------------------------------------------------- Q5. Average marks section A of class 9 is 70 and average marks of section B of class 9 is 80. Find the average marks of class 9, assuming: - Both sections have equal students - There are 55 students in section A and there 45 students in section B ```{julia} # Answer ``` ---------------------------------------------------------------------------------------------------------- Q6. $x_1$, $x_2$, $…$, $x_n$ are $n$ values. We are to calculate sum of squared deviation around a number $a$ as follows: $$ SSD = (x_1 - a)^2 + (x_2 - a)^2 + … + (x_n - a)^2 $$ Show that $SSD$ is minimum when *a* is the mean of the given values. ```{julia} # Answer ``` --------------------------------------------------------------------------------------------------------------- Q7. Median is not affective by extreme values. Give examples in support of your answer. ```{julia} # Answer ``` --------------------------------------------------------------------------------------------------------------- Q8. Somnath does data analysis for a company. The data on tea consumption (in grams) for the company are as follows: 14.77 16.11 16.11 15.05 15.99 14.91 15.27 16.01 15.75 14.89 16.05 15.22 16.02 15.24 16.11 15.02 - Calculate the mean and median tea consumption. - Which of the mean and median measures is best to use? Explain ```{julia} # Answer ``` ------------------------------------------------------------------------------------------------------ Q9. Following are the responses from 55 employees to the question about how much time they travel to reach the office (in mins). 055 060 080 080 080 085 085 085 090 090 090 090 092 094 095 095 095 095 100 100 100 100 100 100 105 105 105 105 109 110 110 110 110 112 115 115 115 115 115 120 120 120 120 120 124 125 125 125 130 130 140 140 140 145 150 Calculate the range and interquartile range and interpret your result. ```{julia} # Answer ``` ---------------------------------------------------------------------------------------------------------- Q10. An agriculture farm sells grab bags of flower bulbs. The bags are sold by weight; thus the number of bulbs in each bag can vary depending on the varieties included. Below are the number of bulbs in each of the 20 bags sampled: 21 33 37 56 47 25 33 32 47 34 36 23 26 33 37 26 37 37 43 45 - What are the mean and median number of bulbs per bag? - Based on your answer, what can you conclude about the shape of the distribution of number of bulbs per bag? ```{julia} # Answer ``` ---------------------------------------------------------------------------------------------------------- Q11. The wholesale prices of a commodity for a week are as follows: Days: 1 2 3 4 5 6 7 Commodity `price/kg`: 240 260 270 245 255 286 264 Calculate the variance and standard deviation. ```{julia} # Answer ``` ------------------------------------------------------ Q12. (Continue from Q11) Suppose for next week, `price/kg` is just 10 more than previous week. Calculate the variance and standard deviation. What is your conclusion? ```{julia} # Answer ``` --------------------------------------------------------------------------------------